In the present paper we proposed a novel stage cost for Funnel MPC and proved that the resulting FMPC Algorithm REF  is initially and recursively feasible. This extends earlier approaches from [1]}, [2]} to nonlinear systems with arbitrary relative degree and belonging to the system class \(\mathcal {N}^{m,r}\) . Although we didn't require any terminal conditions or a sufficiently long prediction horizon (as in [3]} for relative degree two), we imposed an additional feasibility constraint in the OCP (REF ). This constraint does not only restrict the set of admissible controls, but the required parameters \(\varepsilon _1,\ldots ,\varepsilon _r\in (0,1)\)  and \(M>0\)  provided by Proposition REF  are usually quite conservative and hard to compute. Further research should focus on relaxing the OCP by removing the feasibility constraints.
